x(2x-6)4=(2x+4)(x-4)

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Solution for x(2x-6)4=(2x+4)(x-4) equation: 


Simplifying
x(2x + -6) * 4 = (2x + 4)(x + -4)

Reorder the terms:
x(-6 + 2x) * 4 = (2x + 4)(x + -4)

Reorder the terms for easier multiplication:
4x(-6 + 2x) = (2x + 4)(x + -4)
(-6 * 4x + 2x * 4x) = (2x + 4)(x + -4)
(-24x + 8x2) = (2x + 4)(x + -4)

Reorder the terms:
-24x + 8x2 = (4 + 2x)(x + -4)

Reorder the terms:
-24x + 8x2 = (4 + 2x)(-4 + x)

Multiply (4 + 2x) * (-4 + x)
-24x + 8x2 = (4(-4 + x) + 2x * (-4 + x))
-24x + 8x2 = ((-4 * 4 + x * 4) + 2x * (-4 + x))
-24x + 8x2 = ((-16 + 4x) + 2x * (-4 + x))
-24x + 8x2 = (-16 + 4x + (-4 * 2x + x * 2x))
-24x + 8x2 = (-16 + 4x + (-8x + 2x2))

Combine like terms: 4x + -8x = -4x
-24x + 8x2 = (-16 + -4x + 2x2)

Solving
-24x + 8x2 = -16 + -4x + 2x2

Solving for variable 'x'.

Reorder the terms:
16 + -24x + 4x + 8x2 + -2x2 = -16 + -4x + 2x2 + 16 + 4x + -2x2

Combine like terms: -24x + 4x = -20x
16 + -20x + 8x2 + -2x2 = -16 + -4x + 2x2 + 16 + 4x + -2x2

Combine like terms: 8x2 + -2x2 = 6x2
16 + -20x + 6x2 = -16 + -4x + 2x2 + 16 + 4x + -2x2

Reorder the terms:
16 + -20x + 6x2 = -16 + 16 + -4x + 4x + 2x2 + -2x2

Combine like terms: -16 + 16 = 0
16 + -20x + 6x2 = 0 + -4x + 4x + 2x2 + -2x2
16 + -20x + 6x2 = -4x + 4x + 2x2 + -2x2

Combine like terms: -4x + 4x = 0
16 + -20x + 6x2 = 0 + 2x2 + -2x2
16 + -20x + 6x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
16 + -20x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -10x + 3x2) = 0

Factor a trinomial.
2((4 + -3x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {1.333333333, 2}

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